Heat transfer for non-Newtonian laminar flow in internally finned pipes with uniform temperature

An analysis is presented for fully developed laminar convective heat transfer of non-Newtonian power-law fluids in pipes with internal longitudinal fins and uniform outside wall temperature. The governing momentum and energy equations have been solved numerically, with the influence of fin conductance. The distributions of fin temperature, fluid temperature and local heat flux (both at finned and unfinned surfaces) are presented. These are shown to be strongly dependent on finned pipe geometry, fluid flow behavior index and the fin conductance. Values of overall Nusselt number indicated significant heat transfer enhancement over finless pipes. The flow behavior index affects the no. of fins which maximizes the overall Nusselt number.     

Variable viscosity and slip velocity effects on the flow and heat transfer of a power-law fluid over a non-linearly stretching surface with heat flux and thermal radiation

The flow and heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching surface has been studied numerically under conditions of constant heat flux and thermal radiation and evaluated for the effect of wall slip. The governing partial differential equations are transformed into a set of coupled non-linear ordinary differential equations which are using appropriate boundary conditions for various physical parameters. The remaining set of ordinary differential equations is solved numerically by fourth-order Runge–Kutta method using the shooting technique. The effects of the viscosity, the slip velocity, the radiation parameter, power-law index, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin friction and Nusselt numbers are presented. Comparison of numerical results is made with the earlier published results under limiting cases.     

Free convection through conducting non-Newtonian fluids over a thin axisymmetric body

An analysis of free convection heat transfer in electrically conducting power law non-Newtonian fluid over a thin axisymmetric body of constant temperature is carried out. The uniform external magnetic field acts normally to the surface through the induced boundary layer. In view of the fact that most of the non-Newtonian fluids have large Prandtl number, the momentum equation is simplified. The equations of conservation of mass, momentum and energy which govern and describe the flow and heat transfer are solved numerically. The effect of the magnetic field on the velocity, temperature, the coefficient of friction and the Nusselt number are investigated. Numerical results are tabulated, presented graphically and discussed.     

The Falkner–Skan Wedge Flows of Power-Law Fluids Embedded in a Porous Medium

The non-Darcy flow characteristics of power-law non-Newtonian fluids past a wedge embedded in a porous medium have been studied. The governing equations are converted to a system of first-order ordinary differential equations by means of a local similarity transformation and have been solved numerically, for a number of parameter combinations of wedge angle parameter m, power-law index of the non-Newtonian fluids n, first-order resistance A and second-order resistance B, using a fourth-order Runge–Kutta integration scheme with the Newton–Raphson shooting method. Velocity and shear stress at the body surface are presented for a range of the above parameters. These results are also compared with the corresponding flow problems for a Newtonian fluid. Numerical results show that for the case of the constant wedge angle and material parameter A, the local skin friction coefficient is lower for a dilatant fluid as compared with the pseudo-plastic or Newtonian fluids.     

Steady mixed convection flow of Maxwell fluid over an exponentially stretching vertical surface with magnetic field and viscous dissipation

The steady mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent Maxwell fluid in the presence of magnetic field, viscous dissipation and Joule heating have been studied. The stretching velocity, surface temperature and magnetic field are assumed to have specific exponential function forms for the existence of the local similarity solution. The coupled nonlinear ordinary differential equations governing the local similarity flow and heat transfer have been solved numerically by Chebyshev finite difference method. The influence of the buoyancy parameter, viscous dissipation, relaxation parameter of Maxwell fluid, magnetic field and Prandtl number on the flow and heat transfer has been considered in detail. The Nusselt number increases significantly with the Prandtl number, but the skin friction coefficient decreases. The Nusselt number slightly decreases with increasing viscous dissipation parameter, but the skin friction coefficient slightly increases. Maxwell fluid reduces both skin friction coefficient and Nusselt number, whereas buoyancy force enhances them.     

Effects of viscous dissipation and heat generation (absorption) in a thermal boundary layer of a non-Newtonian fluid over a continuously moving permeable flat plate

The problem of boundary-layer flow and heat transfer of a non-Newtonian power-law fluid over a moving porous infinite flat plate in the presence of viscous dissipation and heat generation or absorption is investigated analytically. It is assumed that both the momentum and the energy equations are coupled by the stress friction factor, and an assumption is introduced regarding the heat-transfer index. It is found that exact analytical solutions for velocity and temperature exist only for pseudoplastic fluids in the presence of suction at the surface. The effects of the suction parameter, Eckert number, and the heat generation or absorption parameter on the velocity and temperature profiles, as well as on the skin-friction coefficient and Nusselt number are discussed.     

Viscous dissipation and thermal radiation effects on the magnetohydrodynamic (MHD) flow and heat transfer over a stretching slender cylinder

An axisymmetric magnetohydrodynamic (MHD) boundary layer flow and heat transfer of a fluid over a slender cylinder are investigated numerically. The effects of viscous dissipation, thermal radiation, and surface transverse curvature are taken into account in the simulations. For this purpose, the governing partial differential equations are transformed to ordinary differential equations by using appropriate similarity transformations. The resultant ordinary differential equations along with appropriate boundary conditions are solved by the fourth-order Runge–Kutta method combined with the shooting technique. The effects of various parameters on the velocity and temperature profiles, local skin friction coefficient, and Nusselt number are analyzed.     

Free-convection boundary-layer flow of a non-Newtonian fluid along a vertical wavy surface

A theoretical analysis of laminar free-convection flow over a vertical isothermal wavy surface in a non-Nevvtonian power-law fluid is considered. The governing equations are first cast into a nondimensional form by using suitable boundary-layer variables that substract out the effect of the wavy surface from the boundary conditions. The boundary-layer equations are then solved numerically by a very efficient implicit finite-difference method known as the Keller-Box method. A sinusoidal surface is used to elucidate the effects of the power-law index, amplitude wavelength, and Prandtl number on the velocity and temperature fields, as well as on the local Nusselt number. It is shown that the local Nusselt number varies periodically along the wavy surface. The wave-length of the local Nusselt number variation is half that of the wavy surface, irrespective of whether the fluid is a Newtonian fluid or a non-Newtonian fluid. Comparisons with earlier works are also made, and the agreement is found to be very good.     

Effect of thermal conductivity on heat transfer for a power-law non-Newtonian fluid over a continuous stretched surface with various injection parameters

The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governing equations in the present study are solved numerically using the Runge-Kutta method. Through a comparison, results for a special case of the problem show excellent agreement with those in a previous work. Two cases are considered, one corresponding to a cooled surface temperature and the other to a uniform surface temperature. Numerical results show that the thermal conductivity variation parameter, the injection parameter, and the power-law index have significant influences on the temperature profiles and the Nusselt number.     

On thermal boundary layer of a non-Newtonian fluid on a power-law stretched surface of variable temperature with suction or injection

 Heat transfer characteristics of a non-Newtonian fluid on a power-law stretched surface of variable temperature with suction or injection were investigated. Similarity solutions of the laminar boundary layer equations describing heat transfer and fluid flow in a quiescent fluid were obtained and solved numerically. Velocity and temperature profiles as well as the Nusselt number, Nu, were studied for two thermal boundary conditions; uniform surface temperature and variable surface temperature, for different parameters; Prandtl number Pr, temperature exponent b, velocity exponent m, injection parameter d and power-law index n. It was found that decreasing injection parameter d, and power-law index n and increasing Prandtl number Pr and surface temperature exponent b enhance the heat transfer coefficient. Received on 27 April 2000     

Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet

An analysis is made for the steady mixed convection boundary layer flow near the two-dimensional stagnation-point flow of an incompressible viscous fluid over a stretching vertical sheet in its own plane. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the stagnation-point. Two equal and opposite forces are impulsively applied along the x-axis so that the wall is stretched, keeping the origin fixed in a viscous fluid of constant ambient temperature. The transformed ordinary differential equations are solved numerically for some values of the parameters involved using a very efficient numerical scheme known as the Keller-box method. The features of the flow and heat transfer characteristics are analyzed and discussed in detail. Both cases of assisting and opposing flows are considered. It is observed that, for assisting flow, both the skin friction coefficient and the local Nusselt number increase as the buoyancy parameter increases, while only the local Nusselt number increases but the skin friction coefficient decreases as the Prandtl number increases. For opposing flow, both the skin friction coefficient and the local Nusselt number decrease as the buoyancy parameter increases, but both increase as Pr increases. Comparison with known results is excellent.     

Non-uniform heat generation effect on heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching sheet

The effects of non-uniform heat generation/absorption and viscous dissipation on heat transfer of a non-Newtonian power-law fluid on a non-linearly stretching surface have been examined. The governing nonlinear partial differential equations describing the problem are transformed to a system of non-linear ordinary differential equations by using suitable similarity transformation. The transformed system of ordinary differential equations is solved numerically using fourth order Runge-Kutta method with the shooting technique. Graphical solutions for the dimensionless temperature are presented and discussed for various values of the power-law index parameter, the Prandtl number, the heat generation/absorption parameter and the Eckert number. The results show that the local Nusselt number is reduced with increasing the Eckert number or the heat generation parameter, whereas the heat absorption parameter has the effect of enhancing the local Nusselt number.     

Mixed Convection in Non-Newtonian Fluids Along an Isothermal Vertical Cylinder in a Porous Medium

Mixed convection in power-law type non-Newtonian fluids along an isothermal vertical cylinder in porous media is studied. The problem is solved by means of a finite difference method for the case of uniform wall temperature. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The viscosity index ranged from 0.5–1.5.     

Unsteady mixed convection flow from a rotating vertical cone with a magnetic field

An analysis is developed to study the unsteady mixed convection flow over a vertical cone rotating in an ambient fluid with a time-dependent angular velocity in the presence of a magnetic field. The coupled nonlinear partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The local skin friction coefficients in the tangential and azimuthal directions and the local Nusselt number increase with the time when the angular velocity of the cone increases, but the reverse trend is observed for decreasing angular velocity. However, these are not mirror reflection of each other. The magnetic field reduces the skin friction coefficient in the tangential direction and also the Nusselt number, but it increases the skin friction coefficient in the azimuthal direction. The skin friction coefficients and the Nusselt number increase with the buoyancy force.     

Thermal radiation effect on mixed convection heat and mass transfer of a non-Newtonian fluid over a vertical surface embedded in a porous medium in the presence of thermal diffusion and diffusion-thermo effects

Thermal radiation, thermal diffusion, and diffusion-thermo effects on heat and mass transfer by mixed convection of non-Newtonian power-law fluids over a vertical permeable surface embedded in a saturated porous medium are investigated. The governing equations describing the problem are non-dimensionalized and transformed into a non-similar form. The transformed equations are solved by using the local non-similarity method combined with the shooting technique. The effects of the physical parameters of the problem on the fluid temperature and concentration are illustrated graphically and analyzed. Also, the effects of the pertinent parameters on the local Nusselt number and the local Sherwood number are presented.     

Unsteady MHD mixed convection flow over an impulsively stretched permeable vertical surface in a quiescent fluid

The unsteady mixed convection flow of an incompressible laminar electrically conducting fluid over an impulsively stretched permeable vertical surface in an unbounded quiescent fluid in the presence of a transverse magnetic field has been investigated. At the same time, the surface temperature is suddenly increased from the surrounding fluid temperature or a constant heat flux is suddenly imposed on the surface. The problem is formulated in such a way that for small time it is governed by Rayleigh type of equation and for large time by Crane type of equation. The non-linear coupled parabolic partial differential equations governing the unsteady mixed convection flow under boundary layer approximations have been solved analytically by using the homotopy analysis method as well as numerically by an implicit finite difference scheme. The local skin friction coefficient and the local Nusselt number are found to decrease rapidly with time in a small time interval and they tend to steady-state values for t*≥5. They also increase with the buoyancy force and suction, but decrease with injection rate. The local skin friction coefficient increases with the magnetic field, but the local Nusselt number decreases. There is a smooth transition from the unsteady state to the steady state.     

纳米流体在伸/缩楔体上的MHD流动数值研究

对纳米流体在伸/缩楔体上的磁流体(MHD)流动进行了数值研究。首先,通过相似变换将控制偏微分方程转化为非线性常微分方程组;然后,利用Matlab软件,借助打靶法,结合四阶五常龙格库塔迭代方案进行数值求解;最后,详细讨论了各控制参数对无量纲速度、温度、浓度、表面摩擦系数、局部Nusselt数和局部Sherwood数的影响。结果表明,楔体在拉伸情况下只有唯一解,理论上不会出现边界层分离;而在一定收缩强度范围内存在双解,边界层流动在壁面处可能会出现边界层分离,壁面抽吸会使边界层分离推迟;楔体在拉伸情况下,磁场参数对表面摩擦系数的影响较大,对局部Nusselt数和局部Sherwood数的影响较小。     

Mixed convection stagnation point flow of a micropolar fluid towards a stretching sheet

The mixed convection two-dimensional boundary layer flow of a micropolar fluid near the stagnation point on a stretching vertical sheet is investigated. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the stagnation point. The transformed ordinary differential equations are solved numerically for some values of the parameters involved using a finite-difference scheme known as the Keller-box method. The features of the flow and heat transfer characteristics are analyzed and discussed. Both assisting and opposing flows are considered. Results are presented in terms of the skin friction coefficient and the local Nusselt number with selections of velocity, microrotation and temperature profiles. Dual solutions are found to exist for the opposing flow.     

Melting heat transfer in steady laminar flow over a moving surface

The steady laminar boundary layer flow and heat transfer from a warm, laminar liquid flow to a melting surface moving parallel to a constant free stream is studied in this paper. The continuity, momentum and energy equations, which are coupled nonlinear partial differential equations are reduced to a set of two nonlinear ordinary differential equations, before being solved numerically using the Runge–Kutta–Fehlberg method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. Effects of the melting parameter, moving parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. It is found that the problem admits dual solutions.     

Heat and mass transfer in stagnation-point flow towards a stretching surface in the presence of buoyancy force and thermal radiation

In this paper an analysis has been made to study heat and mass transfer in two-dimensional stagnation-point flow of an incompressible viscous fluid over a stretching vertical sheet in the presence of buoyancy force and thermal radiation. The similarity solution is used to transform the problem under consideration into a boundary value problem of nonlinear coupled ordinary differential equations containing Prandtl number, Schmidt number and Sherwood number which are solved numerically with appropriate boundary conditions for various values of the dimensionless parameters. Comparison of the present numerical results are found to be in excellent with the earlier published results under limiting cases. The effects of various physical parameters on the boundary layer velocity, temperature and concentration profiles are discussed in detail for both the cases of assisting and opposing flows. The computed values of the skin friction coefficient, local Nusselt number and Sherwood number are discussed for various values of physical parameters. The tabulated results show that the effect of radiation is to increase skin friction coefficient, local Nusselt number and Sherwood number.